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Solving integrals/ cosx-sqrt3*sinx

Integral of cosx-sqrt3*sinx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
   0                           
   /                           
  |                            
  |  /           ___       \   
  |  \cos(x) - \/ 3 *sin(x)/ dx
  |                            
 /                             
-pi                            
----                           
 34
$$\int\limits_{- \frac{\pi}{34}}^{0} \left(- \sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$ 
Integral(cos(x) - sqrt(3)*sin(x), (x, -pi/34, 0))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of sine is negative cosine:

      So, the result is:

    1. The integral of cosine is sine:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                      
 |                                                       
 | /           ___       \            ___                
 | \cos(x) - \/ 3 *sin(x)/ dx = C + \/ 3 *cos(x) + sin(x)
 |                                                       
/
$$\int \left(- \sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___     ___    /pi\      /pi\
\/ 3  - \/ 3 *cos|--| + sin|--|
                 \34/      \34/
$$- \sqrt{3} \cos{\left(\frac{\pi}{34} \right)} + \sin{\left(\frac{\pi}{34} \right)} + \sqrt{3}$$ 
=
= 
  ___     ___    /pi\      /pi\
\/ 3  - \/ 3 *cos|--| + sin|--|
                 \34/      \34/
$$- \sqrt{3} \cos{\left(\frac{\pi}{34} \right)} + \sin{\left(\frac{\pi}{34} \right)} + \sqrt{3}$$ 
sqrt(3) - sqrt(3)*cos(pi/34) + sin(pi/34)
Numerical answer [src] 
0.0996569828564339
0.0996569828564339

    Use the examples entering the upper and lower limits of integration.

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